give me an idea ?

i am solving a conjugate heat transfer problem in natural convection using Finite volume method on a staggered grid using SIMPLE. can any one give me an idea as to how to place the control volume faces and grid lines with respect to a square conducting body placed at the geometric centre in a square enclosure . Should i place the control volume lines or the grid lines on the conducting body. if so what extra care should i take in each method .

i have a term kstar(ks/kf) in my solid energy equation . how should i handle the abrupt variation in the value of kstar between fluid and solid

note that i have to satisfy the noslip and heat flux continuity at the fluid/body interface in both the directions